Finite Group Databasebeta

← #101480

Subgroups — #101480

Order 512.

343 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 343 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#29394C211yesmaximal, characteristic
2#21342C211yesmaximal, characteristic
3#9877C211yesmaximal, characteristic
4#7644C211yesmaximal, characteristic
5#7624C211yesmaximal, characteristic
6#7041C211yesmaximal, characteristic
7#7019C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9#2295C2211yescharacteristic
10#2083C411yescharacteristic
11#2072C411yescharacteristic
12#2057C411yescharacteristic
13#2024C411yescharacteristic
14#1985—21no—
15#1940—21no—
16#1928—21no—
17#1921—21no—
18#1921—21no—
19#1917—22no—
20#1863—21no—
21#1839C2211yescharacteristic
22#1839C2211yescharacteristic
23#1831C2211yescharacteristic
24#1768—21no—
25#1767C2211yescharacteristic
26#1746—21no—
27C4×#97C2211yescharacteristic
28#1279—21no—
29#1279—21no—
30#1272—21no—
31#1272—22no—
32#1271—21no—
33C2×C4⋊Q8C2×C411yescharacteristic
34C2×C4×Q8—21no—
35C2×C4×Q8D411yescharacteristic
36C2×#107—21no—
37C2×#107—21no—
38C2×C4⋊C8—22no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×#103—21no—
42C2×#103—21no—
43C2×#97—21no—
44C2×#97—21no—
45C2×#97—21no—
46C2×C4×C8D411yescharacteristic
47C2×C4×C8D411yescharacteristic
48#391—21no—
49#391C2×C411yescharacteristic
50#391D411yescharacteristic
51#389—21no—
52#389—21no—
53#389C2×C411yescharacteristic
54#389D411yescharacteristic
55#387—21no—
56#387—21no—
57#384C2×C411yescharacteristic
58C4×C4⋊C4—21no—
59C4×C4⋊C4—21no—
60C4×C4⋊C4—21no—
61C4×C4⋊C4D411yescharacteristic
62#376—21no—
63C43C2311yescharacteristic
64#340—21no—
65#340—21no—
66#340—21no—
67#340—21no—
68#336—22no—
69#336—22no—
70#336—22no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336C2×C411yescharacteristic
79#336C2×C411yescharacteristic
80#336D412yes—
81C22×Q8—21no—
82C22×Q8C22⋊C411yescharacteristic
83C22×C8—21no—
84C22×C8—21no—
85C22×C8—21no—
86C22×C8—21no—
87C22×C8—22no—
88C22×C8—41no—
89C22×C8—41no—
90C4⋊Q8—42no—
91C4×Q8—41no—
92C4×Q8—41no—
93C4×Q8—82no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4C22⋊C411yescharacteristic
104C2×C4⋊C4C22⋊C411yescharacteristic
105C2×C4⋊C4C22⋊C411yescharacteristic
106C2×C42—21no—
107C2×C42—21no—
108C2×C42—41no—
109C2×C42C22×C411yescharacteristic
110C2×C42C2×D411yescharacteristic
111C2×C42C2×D411yescharacteristic
112C2×C42C2×D411yescharacteristic
113C2×C42C2×D411yescharacteristic
114C2×C42#4111yescharacteristic
115C2×C42#4111yescharacteristic
116#107—42no—
117#107—42no—
118C4⋊C8—41no—
119C4⋊C8—41no—
120C4⋊C8—44no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123#103—42no—
124#103—42no—
125#97—41no—
126#97—41no—
127#97—42no—
128#97—41no—
129#97—41no—
130C4×C8—21no—
131C4×C8—21no—
132C4×C8—21no—
133C4×C8Q1612yes—
134#95—21no—
135#95—21no—
136#95—21no—
137#95—21no—
138#95—21no—
139#95—21no—
140#95—21no—
141#95—41no—
142#95—41no—
143C2×Q8—22no—
144C2×Q8—21no—
145C2×Q8—21no—
146C2×Q8—41no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—81no—
150C2×Q8—81no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4C2×C22⋊C411yescharacteristic
158C22×C4C4×D411yescharacteristic
159C22×C4C4×D411yescharacteristic
160C22×C4#12011yescharacteristic
161C22×C4#12111yescharacteristic
162C22×C4#12111yescharacteristic
163C22×C4#12311yescharacteristic
164C2×C8—22no—
165C2×C8—22no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8—81no—
180C2×C8—81no—
181C2×C8—81no—
182C2×C8—81no—
183C2×C8—81no—
184C2×C8—81no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—42no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—81no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—82no—
201C42—21no—
202C42—21no—
203C42—41no—
204C42—41no—
205C42—41no—
206C42—41no—
207C42—41no—
208C42—42no—
209C42—42no—
210C42—82no—
211C42C2×Q1611yescharacteristic
212C42#13511yescharacteristic
213C42#13711yescharacteristic
214C42#13711yescharacteristic
215C23#38611yescharacteristic
216Q8—42no—
217Q8—81no—
218Q8—82no—
219Q8—82no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4#42111yescharacteristic
256C2×C4#42111yescharacteristic
257C2×C4C4×Q1611yescharacteristic
258C2×C4#44111yescharacteristic
259C2×C4#45111yescharacteristic
260C2×C4#45211yescharacteristic
261C2×C4#46211yescharacteristic
262C2×C4#46411yescharacteristic
263C8—42no—
264C8—42no—
265C8—82no—
266C8—81no—
267C8—81no—
268C8—161no—
269C8—161no—
270C22#187811yescharacteristic
271C22#188111yescharacteristic
272C22#189111yescharacteristic
273C22#189711yescharacteristic
274C22#190311yescharacteristic
275C22#190611yescharacteristic
276C22#190911yescharacteristic
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—81no—
289C4—81no—
290C4—82no—
291C4—81no—
292C4—81no—
293C4—161no—
294C2#904811yescharacteristic
295C2#923611yescharacteristic
296C2#928811yescharacteristic
297C2#931311yescharacteristic
298C2#936911yescharacteristic
299C2#949311yescharacteristic
300C2#953211yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#293942
#213422
#98772
#76442
#76242
#70412
#70192